| 一种完全非线性函数的构造 |
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| 引用本文： | 郭腓望,张习勇,韩文报. 一种完全非线性函数的构造[J]. 山东大学学报(理学版), 2011, 46(3): 26-30,40 |
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| 作者姓名： | 郭腓望 张习勇 韩文报 |
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| 作者单位： | 信息工程大学信息工程学院,河南郑州,450002 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 完全非线性(perfect nonlinear,PN)函数在密码学和代数组合等领域中具有重要的应用价值。从已有的两个基本完全非线性函数出发,通过确定一类有限域上线性化多项式方程的解,构造了奇数特征有限域上一类2次完全非线性函数,证明了该函数不等价于形式为x2的完全非线性函数,并通过一个实例分析了它与完全非线性函数xps+1的等价性问题。
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| 关 键 词： | PN函数 APN函数 CCZ等价 EA等价 线性置换 |
A construction of perfect nonlinear functions |
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| GUO Fei-wang,ZHANG Xi-yong,HAN Wen-bao. A construction of perfect nonlinear functions[J]. Journal of Shandong University, 2011, 46(3): 26-30,40 |
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| Authors: | GUO Fei-wang ZHANG Xi-yong HAN Wen-bao |
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| Affiliation: | GUO Fei-wang,ZHANG Xi-yong,HAN Wen-bao(Institute of Information Engineering,Information Engineering University,Zhengzhou 450002,Henan,China) |
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| Abstract: | Perfect nonlinear functions are widely used in cryptography and algebra combinatorics.By using two known perfect nonlinear functions,a quadratic perfect nonlinear function over finite fields of odd characteristic was constructed based on determining the root of a linearized function.This quadratic function was proved to be inequivalent to x2,and then an example was used to analyzed its inequivalence to xps+1. |
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| Keywords: | perfect nonlinear function almost perfect nonlinear function CCZ-equivalence EA-equivalence linearized permutation |
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